then the "arithmetical demons," or steps of special difficulty, as well as the minor difficulties which they encounter. Upon this basis a thorough systematic drill system in arithmetic may be worked out, printed upon sheets, and made available for all teachers. Thousands of hours have been spent by men of scientific ability, coöperating with teachers all over the country, in devising and revising such arithmetical drill systems. They are now for sale by publishers. If a teacher is at work in a school which, unfortunately, does not provide her with such ready-made drill systems for use in her classes, it would pay her to secure sample copies of them in order to derive many suggestions for improving her drill lessons. For a list of some of these ready-made systems see the bibliography at the end of this chapter. 5. Continue drill until precise standard scores are maintained. — The scientific drill systems described above enable us to answer a very perplexing question; namely, When has sufficient drill been given on any combination or operation in reading, handwriting, or arithmetic? This question is puzzling for two reasons. In the first place, a child may be able to read or write or cipher satisfactorily at a slow speed but make mistakes at a higher speed. We can increase his speed by well-organized practice or drill, but we need to know when it has reached a sufficient rate. The question is answered by the scientific drill systems by giving standard scores. For example, the class which was multiplying a certain pack of fraction cards described above would not have sufficient skill until it could finish the pack in three minutes; or, in the case of the arithmetic practice sheets described on page 253, a fifth-grade child who is practicing with the lesson sheets is not permitted to leave each until he can complete correctly all the problems on it in a timed test of seven minutes. These standard scores which the children are expected to attain in any grade have been determined by careful investigations of the scores made by thousands of children in each grade when they have been given various kinds and amounts of training. The scores which they are to attain upon graduation from the eighth grade have been determined by reliable tests of adults who use in daily life the operations or combinations which are to be practiced. - Persistence of skill determined by standard tests. The second puzzling feature of the question of when has sufficient drill been given is the fact that a child may reach a satisfactory score in handwriting or arithmetic to-day, but fall below it next week or next year. The standard drill systems take care of this difficulty by testing the children frequently, several times each year, and determining from their scores just how much drill they need. It is usually found that some children need practice regularly throughout the grades in order to keep them up to standard scores in handwriting and the fundamental operations in arithmetic, but other children retain their skill so permanently, or regain it so quickly, that they may be excused from much of the practice that is necessary for many of the children. This fact will be referred to again in a later chapter on individual differences. 6. Give practice in using abstract forms and processes in concrete situations. Finally, we may emphasize the importance of giving pupils practice in using in concrete, complex situations the abstract forms and operations which they have practiced in isolation in the abstract drills. This process was illustrated in the examples with which this chapter opened, where, in the reading lesson, after the card drill, the children proceeded to read sentences containing the words of the drill, and after the fraction drill the children used multiplication of fractions in solving area problems. One of the simplest examples of the need of such concrete practice is found in the case of spelling, in which a child may spell a new difficult word correctly when it occurs in a column test but spell it incorrectly when writing it in a sentence. Such failures are illustrated in the following experiment by Tidyman and Brown. (6) A sixth-grade class containing 41 pupils was taught the spelling of 37 new words, 20 of these being rated as easy and 17 as difficult. "The method of teaching consisted of the study of the individual words from the board, use in oral sentences, oral spelling, and writing," but the words were not written in sentences during the training. After some weeks, tests were given which included all the new words in column spelling as well as all of them in dictated sentences. The amount of correct spelling of the new words in the sentence test was only 89 per cent of the amount of correct spelling in the column test with the same words; that is, there was a loss of 11 per cent when the words were written in sentences. Large amount of skill transferred, but must correct amount lost. We must not be confused, however, by the above results and conclude that training in column spelling is a waste of time. The fact that the correct spelling in the sentences was 89 per cent as great as in the columns is probably more impressive than the loss of II per cent. It shows that spelling words may be learned in isolation and then correctly used in sentence writing, with very small loss. However, since our purpose is to secure absolute correctness in sentence spelling, we should not overlook this small loss, but take steps to correct it by giving practice in writing the words in sentences in addition to the spelling of the words in isolation. Rules for conduct of drills briefly phrased. The above pages present the fundamental principles and rules to be observed in conducting drill lessons. They may be phrased briefly in the following words: 1. Only correct practice makes perfect. a. Make a correct start. b. Subordinate speed to accuracy. 2. Avoid unnecessary processes. 3. Arouse zeal and interest. 4. Use ready-made scientific drill systems. 5. Drill till standard scores are maintained. 6. Apply abstract forms in concrete situations. Is incidental drill as good as socially valuable, interesting, scientifically organized specific drill? — It is generally admitted at the present time that such specific and scientifically organized drill is desirable and necessary in schools. There are a few educators, however, who think that the necessary skill in reading, handwriting, spelling, and arithmetic can be acquired incidentally during the study of history, geography, literature, manual training, etc. They do not believe in abstract drills upon forms, combinations, and processes in isolation from concrete, complex situations. A great deal of discussion has centered in this question of specific drill versus incidental drill. Three aspects of the question have been disposed of in our earlier discussions and may be summarized as follows: First. The social necessity and value of these forms of skill have been shown by precise, objective studies of social activities in the world at large. These studies determine just what spelling words and arithmetical processes and degrees of speed and accuracy in handwriting are desirable. The studies of spelling and arithmetic were summarized in our chapter on the selection of subject matter (pages 103-106). Second. Children manifest the most intense interest in abstract drills which are so organized as to appeal to their instinctive interests in games and emulation, without recourse to any other motive. This was discussed in our chapter on interests (pages 208 and 239-242). Third. Ten minutes a day of such socially valuable, interesting, well-organized drills have proved sufficient in each subject to maintain high degrees of skill, most of which transfers to concrete situations. Our discussions, therefore, have proved that the abstract processes practiced in scientifically organized isolated drills are socially valuable, that the children may take intense interest in such drills, and that the latter are effective in giving children a command of these abstract tools for use in concrete, complex situations. Inadequacy of incidental practice shown by measured results. It remains for us to determine whether incidental drill, without the specific abstract isolated drill, is equally effective. Scientific tests indicate that it is not, that where children are not given specific drills, their skill in spelling, handwriting, and arithmetic falls far below that which has been shown to be socially desirable and which they can easily attain through specific drill. The Elementary School of The University of Chicago furnishes interesting evidence of these facts, since, up to about 1909, it was conducted largely on the basis of incidental drills, and after that date specific drills were emphasized. The inadequacy of the incidental drill came to light about 1908, when Stone measured with carefully devised tests the efficiency in arithmetic shown by sixth-grade children in twenty-six school systems, including The University of Chicago Elementary School. The latter took very low rank; in fact so unsatisfactory was its showing that its faculty became very much concerned to improve its efficiency in arithmetic by instituting specific drill in arithmetic. As a consequence specific standardized drill in this subject is now emphasized in the school. Similar results came to light in the handwriting. This was tested by Professor Freeman in 1912 and found to rank well below that of a good public-school system. Ten minutes a day of specific drill in handwriting was then introduced and the amount of improvement measured after several months with favorable results. Such scientific measurements show the results of incidental practice in arithmetic and handwriting in an unusually |